2xdx-1-x-4-

Question Number 124398 by bounhome last updated on 03/Dec/20

\int \frac{2 x d x}{\sqrt{1 + x^{4}}} = ?

Answered by Dwaipayan Shikari last updated on 03/Dec/20

\int \frac{2 x d x}{\sqrt{1 + x^{4}}} x^{2} = t \Rightarrow 2 x = \frac{d t}{d x}

= \int \frac{d t}{\sqrt{1 + t^{2}}} = l o g (t + \sqrt{t^{2} + 1}) = l o g (x^{2} + \sqrt{x^{4} + 1}) + C